This is the 15028th most frequent German word.
sehrwohl
"Sehrwohl" means "very well" or "indeed" (often used to emphasize agreement or acknowledgment).
Here, 'sehrwohl' emphasizes the certainty and acknowledgment of the speaker's awareness.
Ich bin mir sehrwohl bewusst, dass dies wichtig ist.
I am indeed well aware that this is important.
'Sehrwohl' is used to affirm the correctness and compliance of her actions.
Sie hat sich sehrwohl an die Regeln gehalten.
She indeed followed the rules well.
In this case, 'sehrwohl' asserts the possibility and encouragement for the subject's stance.